In Old English, may was a finite verb, and might was its past form. Today, in modern English, both are modals, and can be used interchangeably in most situations. The exception is when may used as a verb meaning "wish" (imperative)

"May/might is an example of a modal auxiliary verb. The distinction between may and might has to do with the tense (present, past etc.) and/ or mood (indicative/ subjunctive). "May" is the present indicative and "might" is either the past indicative (which isn't relevant to your particular query) or the past subjunctive. Your question therefore ultimately boils down to a more general question about when to use the present indicative and when to use the past subjunctive of a modal auxiliary verb.

A particular problem is that in certain varieties of spoken English we often use the past subjunctive ("might") when a simple present indicative ("may") is appropriate. This use of the past subjunctive may be acceptable in informal spoken English, but in careful written English you really ought to use the indicative unless the subjunctive is required.

> (1) past indicative [not relevant to your query!] e.g. "Tom might have gone to the Canary Islands last Easter" *might ==> (2) past subjunctive e.g. "If Tom were to win the lottery this year then he might go to the Canary Islands for Christmas". Such usages of the subjunctive can often be rephrased using the indicative mood. Thus - "If Tom wins the lottery this year he may go to the Canary Islands for Christmas." A conditional counterfactual, however, always requires the past subjunctive ("might"). Thus - "If Christmas were in July then Tom might go to the Canary Islands for Christmas"...

...The present indicative "may" already indicates both possibility and permissibility. To imply that the difference between may and might is between permissibility and possibility ... is not correct. As already mentioned the distinction is essentially between the indicative and subjunctive moods...

...Basically you should always use "may" except in the few instances when "might" is appropriate.

"May" has the sense of "being permitted"; e.g. the invigilator of a written examination due to commence at two o'clock would say: "The time is two o'clock; you may commence writing now", meaning "You are permitted to start"... (not "You can start writing now" of course, which means "You are able to start", but that's another issue). "Might" has the sense of something being a possibility, either in the past, present or future. e.g. the same invigilator, if he or she spoke good English, might say:"You might start writing now, but if you do then you will be disqualified, because it is not yet two o'clock". Not only might that same invigilator deliver that warning, but he or she may deliver it, because that is part of his/her duty - invigilators are allowed to inform examinees of correct procedure. Furthermore, the same invigilator might say: "If you start writing before two o'clock I might come over and smack you"; it is possible that he or she is under great duress and has lost it; however, the invigilator may not say that, because no invigilator may smack examinees or threaten to do so. And of course no well-spoken invigilator should say: "If you start writing before two o'clock I may come over and smack you", because that would be a lie - it implies he or she has permission from the Exam Board, and no Exam Board permits invigilators to smack examinees. 1. Mother: "It might rain today". Well-spoken son:"I might take an umbrella, but I lost mine, so it depends on whether I can find one or not. May I borrow yours please?" 2. Mother: "It may rain today". Well-spoken son:"Who do you think you are Mum, telling the clouds what to do? God?"